Cubic spline approximation for weakly singular models

In this paper we propose a numerical collocation method to approximate the solution of linear integral mixed Volterra- Fredholm equations of the second kind, with particular weakly singular kernels. The collocation method is based on the class of quasi-interpolatory splines on locally uniform mesh. These approximating functions are particularly suitable to tackle on problems with weakly regular solutions. We analyse the convergence problems and we present some numeri-cal results and comparisons to confirm the efficiency of the numerical model.